Lab Report: The Simple Pendulum

Gain insight on how scientists come to understand natural phenomena through theoretical and experimental data by determining the Period of a Simple Pendulum. This experiment will introduce us to the processes of data collection and the procedures used for data /error analysis.

Theory:

A Period of motion is a physical quantity associated with any cyclical natural phenomenon and is defined as one complete cycle of motion. There are many examples of this in nature, such as the earth’s period of rotation around the sun takes approximately 365 days.

The Simple Pendulum is a basic time-keeping apparatus. A weight is suspended on a length of string which in turn is attached to a frictionless pivot so it can swing freely. The time period it takes to complete one swing is determined by the theoretical equation derived from the Physical Theory of Repeating Motions, aka Simple Harmonic Motion.

T=2π〖[L⁄g]〗^(1/2)

Where T is the period, L is the length of the pendulum and g is the acceleration due to gravity, g=9.81 m/s^2.

Once finding the theoretical period we when can compare it to experimental measured value we found of the period. In gathering the experimental data there will be a degree of uncertainty associated with the gathered values. Because of the uncertainty in gathering data this must also be applied to the theoretical value of T with the following equation.

∆T=T〖[((1⁄2 ∆L)/L)^(2 )+ ((1⁄2 ∆g)/g)^2]〗^(1/2)

∆T represents the uncertainty of the value T, ∆L represents the uncertainty in the length of string and ∆g represents the uncertainty in the acceleration from gravity.

With these equations we can compare the theoretical value of T with experimental values of T and can find the statistical uncertainly of our results. If the theoretical and experimental values are equal within the uncertainty ranges we can say that the theory has been proven valid. If they aren’t equal there was some error in the experiment or the theory itself.

Equipment and Procedures:

The equipment used in this experiment was a simple pendulum, a wooden meter stick, a PASCO photogate timer, and a digital stopwatch. Our lab assistant had the equipment setup prior to lab so we didn’t assemble it ourselves.

We first used the wooden meter stick to measure the string from where it was tied at the pivot to around the center of the weight and recorded this length, L, in meters. Next we calculated the theoretical period of our simple pendulum. Then proceeded to find experimental values of T with two different methods of measurement: a PASCO photogate timer and a stopwatch.

The PASCO photogate timer records the period of the pendulum directly with the senor at the base of the pendulum and the sensor at precisely the center of where the weight hangs when not swinging. Once the pendulum starts swinging the values are recorded in a table on the computer screen. We recorded this information and calculated the Standard Deviation of the average.

Next we measured the period with a digital stopwatch. One person started the pendulum swinging and another timed 5 oscillations with the stopwatch. We divided the time by 5 and recorded it. This was repeated until we had five Periods at which point we calculated the average of the 10 measurements and calculated the Standard Deviation of the average.

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the period of a simplependulum?”
IBDP PHYSICS Internal Assessment – The SimplePendulum
9
INTRODUCTION
The original aim for this invesigation was to “investigate the simplependulum”. There are many variables
one could look into, such as displacement, angle, damping, mass of the bob etc. The most interesting
variable, however, is the length of the swinging pendulum. The relationship between the length and the
time for one swing (the period) has been researched for many centuries, and has allowed famous
physicists like Isaac Newton and Galileo Galilei to obtain an accurate value for the gravitational
acceleration ‘g’. In this report, we will replicate their experiment, and we will try to find an accurate value
for ‘g’ here in Pisa. We will then compare this value with the commonly accepted value of 9.806 m/s2
[NIST, 2009]
A CLOSER LOOK AT OUR VARIABLES
In this investigation, we varied the length of the pendulum (our independent variable) to observe a
change in the period (our dependent variable). In order to reduce possible random errors in the time
measurements, we repeated the measurement of the period three times for each of the ten lengths. We
also measured the time for ten successive swings to further reduce the errors. The length of our original
pendulum was set at 100 cm and for each...

...﻿
Introduction:
Aim: To find the relationship between the length of a simplependulum and the period of oscillation.
Research question: How does the string length of the pendulum affect the period of oscillation?
Prediction: The longer the string, the longer it will take to make one complete oscillation.
Variables:
Independent variable: Length (L).
Dependent variable: Period of oscillation (T).
Controlled variable: Mass of the plasticine.
Tools & Materials:
Stopwatch.
Ruler.
String.
Plasticine.
Ring Stand.
Pen.
Paper.
Highlighter.
Method:
1. I took the highlighter and put it on the table beside the ring stand so I can control my angle every time I swing the string that has the plasticine at its end.
2. I measured the length of the string 8 times because every time I decrease its length.
3. I take the stopwatch in my hand to record the time of the pendulum doing 10 times a whole complete oscillation.
4. I wrote down every time I record a time on my sheet of paper so that I don’t forget.
Raw data:
1
2
3
4
5
6
7
8
12.22 s
12.03 s
11.36 s
11.13 s
10.60 s
10.14 s
9.68 s
9.17 s
T 10 (±0.01)
12.25 s
11.95 s
11.64 s
11.14 s
10.72 s
10.06 s
9.63 s
9.28 s
12.53 s
11.89 s
11.66 s
11.19 s
10.55 s
10.20 s
9.76 s
9.27 s
1.222 s
1.203 s
1.136 s
1.113 s
1.060 s
1.014 s
0.968 s
0.917 s
T= T10/10
1.225 s
1.195 s
1.164 s
1.114 s
1.072 s
1.006 s...

...EXPERIMENT 2 Measurement of g: Use of a simplependulum
OBJECTIVE: To measure the acceleration due to gravity using a simplependulum.
Textbook reference: pp10-15
INTRODUCTION:
Many things in nature wiggle in a periodic fashion. That is, they vibrate. One such example is a simplependulum. If we suspend a mass at the end of a piece of string, we have a simplependulum. Here, the to and fro motion represents a periodic motion used in times past to control the motion of grandfather and cuckoo clocks. Such oscillatory motion is called simple harmonic motion. It was Galileo who first observed that the time a pendulum takes to swing back and forth through small distances depends only on the length of the pendulum The time of this to and fro motion, called the period, does not depend on the mass of the pendulum or on the size of the arc through which it swings. Another factor involved in the period of motion is, the acceleration due to gravity (g), which on the earth is 9.8 m/s2. It follows then that a long pendulum has a greater period than a shorter pendulum.
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...Introduction
In this lab we had to design a system that would test if changing the mass, angle of release and length would have any effect on the period of a pendulum.
Hypothesis
As the length, mass and angle of release change, the period (T) will change for each one of these factors.
Materials
Lab stand
Protractor
Cardboard
Fishing line
Stopwatch
Weights
Hook for weights
Tape
Ruler
Weighing scale
Logger Pro
Variables
Independent
Angle of release
Dependent
Period
Length of string
Mass of bob
Design
Procedure
First you have to set the lab up as seen above. Draw the protractor on a piece of paper and stick this piece of paper on a cardboard board. Attach this cardboard board to the lab stand with ductape. Attach the string to the lab stand and add the hook with mass to the string.
Then you can start testing the affect of change when the angle of release changes. Look at your protractor and release the pendulum at an angle of 10º. Press the timer as you let go and stop the timer as the bob made a complete cycle. Do this two more times so you have three trials for the release angle of 10º. Then make the angle of release 20º and do three trials again. Change the angel of release with 10º each time for 5 trials.
After testing the affect of change in the angle of release you can start testing the effect of change when you change the...

...SimplePendulum Experiment
In this experiment you will make a simplependulum consisting of a plumb bob and a piece of string anchored at two points. By attaching the string to two points the normal precession that would occur will be eliminated.
[pic]
Items to be turned in as report:
1) all discussion question answers (be thorough)
2) graph of period squared versus length
3) simple data tables of collected data
4) graphical analysis answers
5) using your values for g, calculate average deviation and average percent error (using
9.807 m/s2 as theoretical value)
6) overall conclusions about the experiment (using normal labreport conclusion format)
The SimplePendulum: An Exercise in Measurement and Graphical Analysis
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...PCS125 Lab – The SimplePendulum
Objective and Background
Objective:
The Objective of this experiment is to examine the simple harmonic motion and to determine the value of the acceleration due to gravity from the analysis of the period of the simplependulum. [1]
Background:
There are three equations that will be used to calculate the period of motion of the simplependulum. They are the slope of the line of the graph of T² against L, and the gravity of the pendulum motion. The period of the motion is the time needed for one complete cycle that a pendulum bob swing from the initial position to the other end, and then back to the initial position. [1] The equation to calculate period is,
T = 2πLg
Where,
T = Period of the motion, measured in s.
L = Length of the pendulum, measured in cm.
g = Acceleration due to gravity, measured in m/s2.
The slope of the line in the graph of T² against L can be used to determine the gravity of the pendulum motion. It is because,
y = mx
m = T² L= 4π²g
m = Slope of the line in the graph T²/L.
Therefore, to find the gravity of the pendulum motion, we can use the slope of the graph.
The slope of the graph is given by the formula,
g = 4π²m
g = Acceleration due to gravity, measured in m/s².
Procedure and Observations...

...the period of a pendulum |
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Kyle Butler |
3/1/2011 |
[Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.] |
The effect of mass, angle and length of string on the period of a pendulum
Abstract
The purpose of this lab was to prove the theoretical equation of a pendulum is T=2π(√L/g)and determine if any other factors affect the period of a pendulum. Our hypothesis was that an increase in mass would decrease the period, an increase in angle increase the period and an increase in length of string would increase the period. would a The materials that are needed for this experiment include a photo gate, stand, 10 bobs varying in weight, a role of string, scissors, tape, computer with program for photo gate, protractor, large chart paper, scale, a pencil and a piece of paper. The results produced data with only 6.85% error, we reduced error by using a photo gate and by attempting 3 trials for each set of identical variables and then averaged the results. After the experiment we determined that the period is independent from the mass, that angle may be weakly correlated and that further testing should be done to confirm this point. We also concluded that period is proportional to...

...Is gravity always 9.8m/s2??
INTRODUCTION: A simplependulum consists of a mass m swinging back and forth along a circular arc at the end of a string of negligible mass. A pendulum is a weight suspended from a pivot so that it can swing freely. Gravity is the pull that two bodies of mass exert on one another. There are several simple experiments that will allow you to calculate the acceleration due to gravity of a falling object. A simplependulum can determine this acceleration. The only variables in this experiment are the length of the pendulum (L) and the period of one full swing of the pendulum (T). In this case the independent variable represents the length of the string and the dependent variable represents the period of one oscillation. The control variable is the mass of the pendulum. In this lab our goal was to see if we can prove if the acceleration due to gravity is 9.8m/s2. The R2 in this lab is closed to 9.8 m/s2 . The formula that we used in this lab is T=2πLg and then we solved for g=L(T2π)2.
HYPOTHESIS: The gravity will be 9.81 m/s2 at sea level due to the acceleration.
PROCEDURE:
Materials: stopwatch, meter stick, support stand, string, mass (200g), rod clamp, protractor.
Safety: Be careful not to drop any of the heavy materials or to hit somebody near you by using them.
1. Set...